For Exercises 67-68, find the constants A and B so that the two polynomials are equal. (Hint: Create a system of linear equations by equating the constant terms and by equating the coefficients on the x terms and x 2 terms.) 3 x 2 + 37 x − 82 = A x 2 + A x − 12 A + 3 B x 2 − 10 B x + 3 B + 3 C x 2 + 11 C x − 4 C
For Exercises 67-68, find the constants A and B so that the two polynomials are equal. (Hint: Create a system of linear equations by equating the constant terms and by equating the coefficients on the x terms and x 2 terms.) 3 x 2 + 37 x − 82 = A x 2 + A x − 12 A + 3 B x 2 − 10 B x + 3 B + 3 C x 2 + 11 C x − 4 C
Solution Summary: The author calculates the constants A and B such that the two polynomials are equal.
For Exercises 67-68, find the constants
A
and
B
so that the two polynomials are equal. (Hint: Create a system of linear equations by equating the constant terms and by equating the coefficients on the
x
terms and
x
2
terms.)
3
x
2
+
37
x
−
82
=
A
x
2
+
A
x
−
12
A
+
3
B
x
2
−
10
B
x
+
3
B
+
3
C
x
2
+
11
C
x
−
4
C
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
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